# Decimal and Exponentiation

Tim Peters tim.peters at gmail.com
Sat May 20 21:04:49 CEST 2006

```[Raymond L. Buvel, on
http://calcrpnpy.sourceforge.net/clnumManual.html
]
>>> The clnum module handles this calculation very quickly:
>>>
>>> >>> from clnum import mpf
>>> >>> mpf("1e10000") ** mpf("3.01")
>>> mpf('9.9999999999999999999999932861e30099',26)

[Tim Peters]
>> That's probably good enough for the OP's needs -- thanks!
>>
>> OTOH, it's not good enough for the decimal module:
>>
>>    (10**10000)**3.01 =
>>    10**(10000*3.01) =
>>    10**30100
>>
>> exactly, and the proposed IBM standard for decimal arithmetic requires
>> error < 1 ULP (which implies that if the mathematical ("infinite
>> precision") result is exactly representable, then that's the result
>> you have to get).  It would take some analysis to figure out how much
>> of clnum's error is due to using binary floats instead of decimal, and
>> how much due to its pow implementation.

[Raymond]
> Indeed, it is not clear where the error is comming from especially since
> you can increase the precision of the intermediate calculation and get
> the exact result.
>
> >>> mpf(mpf("1e10000",30) ** mpf("3.01",30), 20)
> mpf('1.0e30100',26)
>
> Is this the kind of thing you will need to do in the Decimal module to
> meet the specification?

It will vary by function and the amount of effort people are willing
to put into implementations.  Temporarily (inside a function's
implementation) increasing working precision is probably the easiest
way to get results provably suffering less than 1 ULP error in the
destination precision.  The "provably" part is the hardest part under
any approach ;-)

```